Normal vector loss.
To further refine the surface of building roof planes, a normal vector loss [1]}, which measures the angles between normal vectors of generated and target gl:DSM, is added to the generator losses:
\(\mathcal {L}_{\text{normal }}\left(\mathcal {N}^{\mathrm {t}}, \mathcal {N}^{\mathrm {p}}\right)=\frac{1}{m} \sum _{i=1}^{m}\left(1-\frac{\left\langle n_{i}^{\mathrm {t}}, n_{i}^{\mathrm {p}}\right\rangle }{\left\Vert n_{i}^{\mathrm {t}}\right\Vert \left\Vert n_{i}^{\mathrm {p}}\right\Vert }\right),\) 
